Question

The differential equation

dydx=72/(y^1/4+64x^2y^1/4)

has an implicit general solution of the form F(x,y)=K, where K
is an arbitrary constant.

In fact, because the differential equation is separable, we can
define the solution curve implicitly by a function in the form

F(x,y)=G(x)+H(y)=K

Find such a solution and then give the related functions requested.

F(x,y)=G(x)+H(y)=

Answer #1

Consider the first order separable equation
y′=12x^3y(1+2x^4)^1/2. An implicit general solution can be written
in the form y=Cf(x) for some function f(x) with C an arbitrary
constant. Here f(x)= Next find the explicit solution of the initial
value problem y(0)=1
y=

Find the general solution of the differential equation
y′′ − 2y′ − 3y = ae3t, where a is a constant

Differential Equations problem
If y1= e^-x is a solution of the differential equation
y'''-y''+2y=0 . What is the general solution of the differential
equation?

Find the general solution to the differential equation
2y'+y=3x

a) Find the general solution of the differential equation
y''-2y'+y=0
b) Use the method of variation of parameters to find the general
solution of the differential equation y''-2y'+y=2e^t/t^3

Find the general solution of the given differential
equation.
y'' − y' − 2y = −8t + 6t2
y(t) =

find the general solution of the differential equation:
y''+2y'+4y=xcos3x

Find the general solution to the differential equation
t^2y'' - 2ty' + 2y = 4

Find the general solution. Express the solution in vector
form.
x' = x + 2y
y' = 4x+3y
Find the general solution. Express the solution in scalar
form.
x' = −4x + 2y
y' = − 5/2 x + 2y

Consider the differential equation y' = x − y + 1:
(a) Verify that y = x + e^(1−x) is a solution to the above
differential equation satisfying y(1) = 2;
(b) Is the solution through (1, 2) unique? Justify your answer
in a few sentences;
(c) Is this differential equation separable? Find the general
solution of y' = x − y + 1.

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